Computing anions have long been understood to offer interesting challenges. For example, anions require diffuse functions for reasonable description. Jensen1 has now investigated the electron affinity of atoms and small molecules with three DFT methods: BHHLYP having 50% HF and 50% Becke exchange, B3LYP having 20% HF and 80% Becke exchange and BLYP with 100% Becke exchange. The result is that all three express varying degrees of electron loss from the atom or molecule in the anion. Thus the anionic species really possess only fractional anionic charge.
In cation-anion pairs or in large species that have strong electron acceptors and donors (say a protein), this electron loss manifests itself in less ionic character than what should actually be present. In other words density is erroneously moved off of the anionic center and transferred to the cationic center.
This error is due to poor description of the long-range exchange. Including the LC correction does eliminate the problem, and so one should be very careful in using DFT for anions.
References
(1) Jensen, F., "Describing Anions by Density Functional Theory: Fractional Electron Affinity," J. Chem. Theory Comput., 2010, 6, 2726-2735, DOI: 10.1021/ct1003324
Henry Rzepa responded on 27 Oct 2010 at 12:16 am #
As Steve notes, adding a long range correction to the functional seems to solve the problem (i.e. LC-BLYP). I wonder whether adding a solvation term might as well? Even the most non polar of solvents can have a profound effect. Frank’s study was pure gas phase, and is therefore not perhaps applicable to studies of reactions occurring in solution. I also note that functionals such as ωB97XD automatically include the long range effects, and the bonus is a more correct treatment of dispersion effects (ion pairs often have many contacts at around the sum of the vdW radii of the atoms involved). Which leads to the next question: do anions have the same dispersion interactions as neutral atoms? I am reminded of a question our crystallographer posed. In refining the electron density maps, he (and everyone else) uses atomic scattering factors which date from the early 1960s, and which (apparently) relate to neutral atoms. He speculates often whether they are appropriate for refining structures where the oxidation states of the atoms are far from zero!
With all these tweaked functionals around, including a variety of often empirical corrections, the functional-zoo is certainly getting more complex. Gone, I suspect, are the days when B3LYP could be used for pretty much everything regardless.
Steven Bachrach responded on 27 Oct 2010 at 7:25 am #
Perhaps one of the attractive early features of DFT was not just its rapid computational time, but the seeming simplification – B3LYP was the magic elixir! Gone was the worry about which post-HF method was needed.
But with the many recent serious concerns about B3LYP (see the many posts I have made), and the proliferation of the functional-zoo, we have stepped backwards and must take the time to choose functionals and benchmarks methods once again.
Frank Jensen responded on 27 Oct 2010 at 2:07 pm #
First let me point out that the paper unfortunately missed a number of important prior contributions by Oleg Vydrov and co-workers, which are very relevant for the problem of fractional electron affinity.
The question of solvation is relevant. For the HCO2- … NH4+ complex, the PCM model appears to produce only one solution, corresponding to a full charge separation. For a large protein, however, the charge separation may occur deeply within the protein, and it is an open question whether a continuum solvation model will make a difference in such a case.
Henry Rzepa responded on 27 Oct 2010 at 3:07 pm #
I would not call it a step backward Steve. We recently looked at a reaction occurring in a large cage (the results will appear in Chem Comm in the near future) comprising four ion pairs, surrounded by water molecules (and ~130 atoms). This would have been a tough system to model a year or so ago. Whilst I hesitate to describe it as routine, the modern methods noted above have made a fantastic difference. Definitely a step forward, not back! And look at the difference these new methods have made to a variety of spectroscopic/chiro-optical predictions!
Steven Bachrach responded on 27 Oct 2010 at 3:56 pm #
My comment of “a step backwards” is in the sense of having a single workhorse method. For a while it seemed that B3LYP might fit that bill – at least for a wide swath of organic chemistry. But now we are faced once again with having to learn which functional is most appropriate for the question at hand. (I think that a lot of the explosion in DFT activity in the 90s could be traced to two developments – nice interfaces to Gaussian and the (indiscriminate) use of B3LYP.)
I completely agree with you that functional development has been amazing in the recent past, and one can, with some study and benchmarking, come upon a suitable method.
Henry Rzepa responded on 28 Oct 2010 at 6:43 am #
Frank asks whether a continuum field would make any difference for charge separated ions deep inside e.g. a protein. Well, the inside of proteins can have very large electric fields. Famously, one can change the pKa of eg a histidine by 2-3 pk units by placing it along the vector of a dipole field generated by an α-helix. I should imagine therefore that ions in such an environment are likely to be heavily influenced by the internal fields. The inside of a protein may therefore be as different from the gas-phase situation as a PCM model is.